Name: measurement error: reading results correctly
Uploaded: 2020-09-03T13:38:25.000Z
Duration: 3 min 37 s
Channel: JoVE

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Ohio’s Learning Standards and Model Curriculum

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Chemistry

Structure And Properties Of Matter

Quantifying matter

uncertainty-in-measurement-accuracy-and-precision

Uncertainty in Measurement: Accuracy and Precision

Scientists make repeated measurements of a quantity during experimentation to ensure that their results are accurate and precise.

The accuracy of a measurement is the degree of closeness of the results to the true or accepted value.

Consider two students, A and B, who repeatedly weighed a gold bar known to have a true mass of 10 grams. Student A reported three values － 9.5 grams, 10 grams, and 10.5 grams, while student B reported masses of 8.5 grams, 8.6 grams, and 8.5 grams. Student A reported values closer to the true mass of the bar compared to student B. Thus measurements by student A were, therefore, more &ldquo;accurate&rdquo;.

Precision, on the other hand, is the measure of how closely the results agree with each other, or how reproducible they are. A measurement is said to be precise if it gives highly similar results when repeated under the same conditions. For instance, the values for the mass of the gold bar reported by student B were very similar to one another, as compared to student A. That is &ldquo;precision&rdquo;.

Accuracy and precision are two distinct qualities of measurement which are independent of each other. Thus, a particular set of measurements can be either accurate, or precise, or neither, or both.

The measurements for the mass of the gold bar by student A were more accurate, close to the true value of 10 grams, but not precise, as they were not close to each other. On the contrary, the measurements by student B were precise, but not accurate.

Highly accurate values tend to be precise too. Like a weighing balance showing true or close to true masses for all the objects, repeatedly. However, highly precise measurements may not necessarily be accurate;&nbsp;if the same balance is improperly calibrated, it may give precise but inaccurate readings. This may lead to scientific errors.&nbsp;

Errors in the measurement process is a common problem. Such errors may fall into two categories － random and systematic.&nbsp;

Random errors are the result of inconsistency in the measuring process or variations in the quantity being measured. These result in fluctuations, too high or too low, around the true value.&nbsp;Consider a scientist measuring the length of an earthworm using a caliper. Inconsistency of the scientist to read the scales correctly, or continuous body movement of the earthworm during the measurement, may result in incorrect length measurements. Random error cannot be avoided, however, it can be averaged out with repeated trials.

Systematic errors are the results of a persistent issue and lead to a consistent discrepancy in measurement. These errors tend to be either all too high or all too low compared to the true value. For instance, weights being measured using an improperly calibrated weighing balance.&nbsp;These are predictable and mostly instrument-related. However, unlike random error, it cannot be averaged out with repeated measurement. 
&nbsp;

uncertainty in measurement: accuracy and precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.&nbsp;

Suppose a quality control chemist at a pharmaceutical company is tasked with checking the accuracy and precision of three different machines, meant to dispense 500 mL of cough syrup into storage bottles. The chemist proceeds to use each machine to fill five bottles and then carefully determines the actual volume dispensed, as reported in Table 1.

<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td colspan="3" style="color: black; border: 1px solid black; text-align: center;">Table 1. Volume (mL) of Cough Syrup Delivered by 500 mL Dispensers</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Dispenser #1</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Dispenser #2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Dispenser #3</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">493.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">502.4</td>
			<td style="color: black; border: 1px solid black; text-align: center;">500.0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">494.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">498.2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">499.8</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">493.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">500.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">500.0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">494.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">498.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">500.1</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">494.2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">494.6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">499.9</td>
		</tr>
	</tbody>
</table>

Considering these results, the chemist reported that dispenser #1 is precise but not accurate. All the values from dispense #1 are close to each other, but none of the values are close to the target value of 500 mL. Results for dispenser #2 showed improved accuracy (values are close to 500 mL) but worse precision (not close to one another). Finally, the chemist reported that dispenser #3 is working well, and it is dispensing cough syrup both accurately (all volumes are within 0.2 mL of the target volume) and precisely (volumes differ from each other by no more than 0.2 mL).

Highly accurate measurements tend to be precise, too. However, highly precise measurements may not necessarily be accurate. For example, an improperly calibrated thermometer or a faulty weighing balance may give precise readings that are inaccurate.

<h4>Random and Systematic Errors</h4>

Scientists always try their best to record their measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors may be random or systematic.

Random errors are observed due to the inconsistency or fluctuation in the measurement process or variations in the quantity itself that is being measured. Such errors fluctuate from too high or too low from the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a ruler. Random error in this measuring process might be the result of the inconsistent method in which the scientist reads the scales, or if the earthworm isn&rsquo;t still and its body movements might pose difficulty in taking correct length measurements. Random error cannot be avoided; however, it can be averaged out with repeated trials.

Systematic errors arise from a persistent issue and result in a consistent discrepancy in measurement. These errors tend to be consistently either too high or too low from the true value. These are predictable and are mostly instrumental in nature. For instance, an improperly calibrated weighing balance may consistently weigh objects heavier than their true value. However, unlike random error, systemic errors cannot average out with repeated measurements.

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision.</a>

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy ...

Education

JoVE Core

Introduction: Matter and Measurement

KEY TERMS AND CONCEPTS

measurement error: reading results correctly

Measurement error affects how scientists judge the quality of their results. Repeated measurements help show whether results are precise and accurate. A measurement is precise when repeated values are very similar. A measurement is accurate when it is very close to the true or accepted value. Precise values agree with each other, while accurate values agree with the true value.

A pharmaceutical quality control chemist can use this idea to check machines that dispense 500 mL of cough syrup. The chemist fills five bottles with each dispenser and then measures the actual volume in each one. Dispenser #1 gives values that stay close together, so it is precise, but the values are far from 500 mL, so it is not accurate. Dispenser #2 gives volumes closer to 500 mL, so it is more accurate, but the results are less consistent. Dispenser #3 performs well because it is both accurate and precise.

Accurate measurements often tend to be precise as well. However, precise measurements are not always accurate. An improperly calibrated thermometer or a faulty weighing balance can give readings that look consistent but are still wrong. This is why repeated measurements and careful checking matter in science.

Measurement error can be random or systematic. Random errors come from changes in the measuring process or from variation in what is being measured. For example, a scientist measuring an earthworm with a ruler may see small changes because of the reading method or because the worm moves. Random error cannot be avoided, but repeated trials can help average it out.

Systematic errors come from a persistent problem and cause measurements to stay consistently too high or too low. These errors are predictable and are often caused by instruments. A balance that is not properly calibrated may always weigh objects heavier than they really are. Unlike random error, systematic error does not average out with repeated measurements.

Measurement Error: Reading Results Correctly

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scientific laws and theories

How Science Explains Laws and Theories

Scientific laws and scientific theories describe science in two different ways. A law is a concise verbal or mathematical statement that summarizes many experimental observations. It describes or predicts aspects of the natural world that stay the same under the same conditions. A scientific theory is different because it explains why natural events happen. It is a unifying principle that gives a well-supported and testable explanation for a broad set of observations. Strong theories are the...

the scientific method

How Scientists Test a Hypothesis

Chemistry uses the scientific method to turn observations into testable answers. Scientists begin by observing a phenomenon in the physical world and then asking a question about it. This process helps explain everyday chemistry through evidence. A question leads to a hypothesis, which is a tentative explanation for what is being observed. Scientists often use earlier research and published literature to shape that idea. A strong hypothesis must be testable, meaning it can be supported by...

physical and chemical properties of matter

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Distinguishing Physical and Chemical Changes

Matter can be identified by its properties, which are the features that help us tell one substance from another. These properties fall into two main groups: physical properties and chemical properties. Understanding the difference helps explain how matter changes. A physical property is a feature of matter that is not linked to a change in chemical composition. Examples include density, color, hardness, melting point, boiling point, and electrical conductivity. Some physical properties can be...

classifying matter by state

States of Matter and Their Properties

States of matter help describe how matter behaves in chemistry. Matter is anything that has mass and takes up space. It is found everywhere, including air, water, soil, mountains, and even our bodies. The three common states on Earth are solid, liquid, and gas. A solid has a definite shape and a definite volume. Its particles, such as atoms or molecules, are packed very closely together and held in place by strong forces, so they only vibrate slightly. This tight arrangement makes solids...

what is energy?

Energy Forms and Conservation

Energy is a property of matter that appears in many forms. On Earth, most energy starts with the Sun. Plants capture light energy from the Sun and use photosynthesis to turn it into chemical energy. That stored energy can then move through living things and materials in several ways. People get energy from plant foods, and wood or coal, which come from fossilized plants, can be burned to produce heat and electricity. Energy is defined as the ability to do work. Work happens when a force moves...

measurement: standard units

Measurement: SI Units and Conversions

Measurement gives three kinds of information: a number, a unit, and an estimate of uncertainty. The number shows size or magnitude. The unit gives a standard for comparison. The uncertainty reflects possible error in the measurement. Numbers can be written in more than one way. A value may appear in decimal form or in scientific notation, which is also called exponential notation. For example, the maximum take-off weight of a Boeing 777-200ER airliner is 298,000 kilograms, or 2.98 × 10^5 kg. <br...

classifying matter by composition

Matter: Elements, Compounds, and Mixtures

Matter can be grouped by composition into pure substances and mixtures. A pure substance has a constant composition throughout and uniform properties. For example, any sample of sucrose has the same composition and the same physical properties, such as melting point, color, and sweetness, no matter where it is isolated from. A mixture contains two or more kinds of matter in varying amounts. Its parts can be separated by physical changes, such as evaporation. The components keep their own...

measurement: derived units

SI Units, Density, and Property Types

SI units and derived units help describe physical properties in chemistry. The International System of Units, or SI system, uses agreed-upon base units for seven fundamental properties: length, mass, time, temperature, electric current, amount of substance, and luminosity. Units made by combining these base units are called SI-derived units. Speed is one example. If distance is measured in meters and time in seconds, the derived unit for speed is meters per second, or m/s. Miles per hour is...

dimensional analysis

Using Conversion Factors to Cancel Units

Dimensional analysis is a method for using conversion factors to cancel units and solve measurement problems. It is also called the factor label method. The main rule is that units must be treated the same way as the numbers attached to them. A conversion factor is a ratio of two equal quantities written in different units. For example, 1 meter is equal to 1.0936 yards. That relationship can be used to build a factor that converts one unit into the other. When a value is multiplied or divided...

Measurement error affects how scientists judge the quality of their results. Repeated measurements help show whether results are precise and accurate. A measurement is precise when repeated values are very similar. A measurement is accurate when it is very close to the true or accepted value. Precise values agree with each other, while accurate values agree with the true value. A pharmaceutical quality control chemist can use this idea to check machines that dispense 500 mL of cough syrup. The...

uncertainty in measurement: reading instruments

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Measurement Uncertainty and Significant Figures

Measurement uncertainty and significant figures show how carefully a value can be read from an instrument. Counting is different. If the number of objects does not change during counting, the result is exact. Defined quantities are exact too. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Most other measurements are not exact because the measuring process has limits. The result depends on the device used and on the person...

uncertainty in measurement: significant figures

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Significant Figures and Rounding Rules

Significant figures and rounding rules help students report measurements with the right level of certainty. A measurement includes every digit that was actually measured, including the last uncertain digit. That is why a value can look simple but still carry useful information about the tool used to measure it. Zero can also be significant when it is part of a measured value. For example, if a scale reads 140 pounds to the nearest pound, the 1, 4, and 0 are all significant. Reporting...

key terms and concepts

Learn how repeated measurements reveal accuracy, precision, random error, and systematic error using simple examples like syrup dispensers, rulers, and balances.

Measurement Error: Reading Results Correctly | JoVE K12

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The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

The Aufbau Principle and Hund's Rule

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Electron Configuration of Multielectron Atoms

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Thomson's e/m Experiment

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Atomic structure
• Evolution of atomic models/theory
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Content elaboration: Physical Science included properties and locations of protons, neutrons and electrons, atomic number, mass number, cations and anions, isotopes and the strong nuclear force which holds the nucleus together. In this course, the historical development of the atomic model and the positions of electrons are explored in greater detail. Atomic models are constructed to explain experimental evidence and make predictions. The changes in the atomic model over time exemplify how scientific knowledge changes as new evidence emerges and how technological advancements like electricity extend the boundaries of scientific knowledge. Thompson's study of electrical discharges in cathode-ray tubes led to the discovery of the electron and the development of the plum pudding model of the atom. Rutherford's experiment, in which he bombarded gold foil with a-particles, led to the discovery that most of the atom consists of empty space with a relatively small, positively charged nucleus. Bohr used data from atomic spectra to propose a planetary model of the atom in which electrons orbit the nucleus, like planets around the sun. Later, Schrödinger used the idea that electrons travel in waves to develop a model in which electrons travel randomly in regions of space called orbitals (quantum mechanical model). Based on the quantum mechanical model, it is not possible to predict exactly where electrons are located but there is a region of space surrounding the nucleus in which there is a high probability of finding an electron (electron cloud or orbital). Data from atomic spectra (emission and absorption) gives evidence that electrons can only exist at certain discrete energy levels and not at energies between these levels. Atoms are usually in the ground state where the electrons occupy orbitals with the lowest available energy. However, the atom can become excited when the electrons absorb a photon with the precise amount of energy (indicated by the frequency of the photon) to move to an orbital with higher energy. Any photon without this precise amount of energy will be ignored by the electron. The atom exists in the excited state for a very short amount of time. When an electron drops back down to the lower energy level, it emits a photon that has energy equal to the energy difference between the levels. The amount of energy is indicated by the frequency of the light that is given off and can be measured. Each element has a unique emission and absorption spectrum due to its unique electron configuration and specific electron energy jumps that are possible for that element. Being aware of the quantum mechanical model as the currently accepted model for the atom is important for science literacy as it explains and predicts subatomic interactions, but details should be reserved for more advanced study. Electron energy levels consist of sublevels (s, p, d and f), each with a characteristic number and shape of orbitals. Orbital diagrams and electron configuration can be constructed to show the location of the electrons in an atom using established rules. Valence electrons are responsible for most of the chemical properties of elements. In this course, electron configuration (extended and noble gas notation) and orbital diagrams can be shown for any element in the first three periods. Although the quantum mechanical model of the atom explains the most experimental evidence, other models can still be helpful. Thinking of atoms as indivisible spheres is useful in explaining many physical properties of substances, such as the state (solid, liquid or gas) of a substance at room temperature. Bohr's planetary model is useful to explain and predict periodic trends in the properties of elements.

Atomic structure

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

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Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

Noble Gases


The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name &ldquo;noble&rdquo; because they were ...

Periodic Table
• Properties
• Trends

Content elaboration: In the Physical Science course, the concept that elements are placed in order of increasing atomic number in the periodic table such that elements with similar properties are placed in the same column is introduced. How the periodic table is divided into groups, families, periods, metals, nonmetals and metalloids is also included and will be revisited here. In this course, with more information about the electron configuration of elements, similarities in the configuration of the valence electrons for a particular group can be observed. The electron configuration of an atom can be determined from the position on the periodic table. The repeating pattern in the electron configuration for elements on the periodic table explains many of the trends in the properties observed. Atomic theory is used to describe and explain trends in properties across periods or down columns including atomic radii, ionic radii, first ionization energies, electronegativities and whether the element is a solid or gas at room temperature. Additional ionization energies, electron affinities and periodic properties of the transition elements, and the lanthanide and actinide series are reserved for more advanced study.

Periodic Table

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

Lewis Symbols and the Octet Rule

Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

The Born-Haber Cycle

Lattice Energy&#xA0;

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a ...

trends-in-lattice-energy-ion-size-and-charge

Trends in Lattice Energy: Ion Size and Charge

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Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Electronegativity

Whether a bond is nonpolar or polar covalent is determined by a property of the bonding atoms called electronegativity.&#xA0;

Electronegativity values of ...

bond-polarity-dipole-moment-and-percent-ionic-character

Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

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lewis-structures-of-molecular-compounds-and-polyatomic-ions

Lewis Structures of Molecular Compounds and Polyatomic Ions

To draw Lewis structures for complicated molecules and molecular ions, it is helpful to follow a step-by-step procedure as outlined:


	Determine the ...

Resonance

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Formal Charges

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Exceptions to the Octet Rule

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	...

Bond Energies and Bond Lengths

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VSEPR Theory and the Basic Shapes

Overview of VSEPR Theory

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VSEPR Theory and the Effect of Lone Pairs

Effect of Lone Pairs of Electrons&nbsp;on Molecule Geometry

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Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries

The following procedure uses VSEPR theory to determine the electron pair geometries and the ...

Molecular Shape and Polarity

Dipole Moment of a Molecule

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Valence Bond Theory

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Hybridization of Atomic Orbitals I

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Hybridization of Atomic Orbitals II

sp3d and sp3d&nbsp;2 Hybridization

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Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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Bonding in Metals

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Chemical bonding
• lonic
• Polar/covalent

Content elaboration: Content in the Physical Science course included recognizing that atoms with unpaired electrons tend to form ionic and covalent bonds with other atoms, forming molecules, ionic lattices or network covalent structures. In this course, electron configuration, electronegativity values and energy considerations will be applied to bonding and the properties of materials with different types of bonding. Atoms of many elements are more stable when they are bonded to other atoms. In such cases, as atoms bond, energy is released to the surroundings, resulting in a system with lower energy. An atom's electron configuration, particularly the valence electrons, determines how an atom interacts with other atoms. Molecules, ionic lattices and network covalent structures have different, yet predictable, properties that depend on the identity of the elements and the types of bonds formed. Differences in electronegativity values can be used to predict where a bond fits on the continuum between ionic and covalent bonds. The polarity of a bond depends on the electronegativity difference and the distance between the atoms (bond length). Polar covalent bonds are introduced as an intermediary between ionic and pure covalent bonds. The concept of metallic bonding is also introduced to explain many of the properties of metals (e.g., conductivity). Since most compounds contain multiple bonds, a substance may contain more than one type of bond. Carbon atoms can bond together and with other atoms, especially hydrogen, oxygen, nitrogen and sulfur, to form chains, rings and branching networks that are present in a variety of important compounds, including synthetic polymers, fossil fuels and the large molecules essential to life.

Chemical bonding

Chemical Formulas

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ionic-compounds-formulas-and-nomenclature

Ionic Compounds: Formulas and Nomenclature

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Molecular Compounds: Formulas and Nomenclature

Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular ...

Organic Compounds

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Classification of Elements and Compounds

Pure substances consist of only one type of matter. A pure substance can be an element or a compound. An element consists of only one type of atom, while ...

Molecular Models

Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models ...

Representing compounds
• Formula writing
• Nomenclature
• Models and shapes (Lewis structures, ball and stick, molecular geometries)

Content elaboration: Using the periodic table, formulas of ionic compounds containing specific elements can be predicted. This can include ionic compounds made up of elements from groups 1, 2, 17, hydrogen, oxygen and polyatomic ions (given the formula and charge of the polyatomic ion). Given the formula, a compound can be named using conventional systems that include Greek prefixes and Roman numerals where appropriate. Given the name of an ionic or covalent substance, formulas can be written. Many different models can be used to represent compounds including chemical formulas, Lewis structures, and ball and stick models. These models can be used to visualize atoms and molecules and to predict the properties of substances. Each type of representation provides unique information about the compound. Different representations are better suited for particular substances. Lewis structures can be drawn to represent covalent compounds using a simple set of rules and can be combined with valence shell electron pair repulsion (VSEPR) theory to predict the three-dimensional electron pair and molecular geometry of compounds. Lewis structures and molecular geometries will only be constructed for the following combination of elements: hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur and the halogens.

Representing compounds

Measurement: Standard Units

Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement ...

Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, ...

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such ...

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a ...

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach ...

Elements: Chemical Symbols and Isotopes

A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Quantifying matter

Content elaboration: In earlier grades, properties of materials were quantified with measurements that were always associated with some error. In this course, scientific protocols for quantifying the properties of matter accurately and precisely are studied. Using the International System of Units (SI), significant digits or figures, scientific notation, error analysis and dimensional analysis are vital to scientific communication. There are three domains of magnitude in size and time: the macroscopic (human) domain, the cosmic domain and the submicroscopic (atomic and subatomic) domain. Measurements in the cosmic domain and submicroscopic domains require complex instruments and/or procedures. Matter can be quantified in a way that macroscopic properties such as mass can reflect the number of particles present. Elemental samples are a mixture of several isotopes with different masses. The atomic mass of an element is calculated given the mass and relative abundance of each isotope of the element as it exists in nature. Because the mass of an atom is very small, the mole is used to translate between the atomic and macroscopic levels. A mole is equal to the number of atoms in exactly 12 grams of the isotope carbon-12. The mass of one mole of a substance is equal to its molar mass in grams. The molar mass for a substance can be used in conjunction with Avogadro's number and the density of a substance to convert between mass, moles, volume and number of particles of a sample.

Measurement Error: Reading Results Correctly

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